pal.statistics
Class BootstrapStatistics

java.lang.Object
  pal.statistics.BootstrapStatistics

public class BootstrapStatistics
extends java.lang.Object

computation of bootstrap estimators (BIAS, SD, VAR, CI) given a statistic theta and corresponding bootstrap replicates. See for background theory: i) B. Efron and R. J.Tibshirani. 1993. An introduction to the bootstrap. Chapman and Hall, New York ii) P. Hall. 1992. The bootstrap and Edgeworth expansion. Springer, New York

Version:

$Id: BootstrapStatistics.java,v 1.3 2001/07/13 14:39:13 korbinian Exp $

Author:

Korbinian Strimmer

Constructor Summary

BootstrapStatistics()

Method Summary

static double	biasCorrectedEstimate(double thetaHat, double[] thetaHatStar) correct a statistic thetaHat for its bias
static double	computeBIAS(double thetaHat, double[] thetaHatStar) compute bias of a statistic thetaHat in estimating the true theta
static double	computeSD(double[] thetaHatStar) compute standard error (accuracy) of a statistic thetaHat
static double	computeVAR(double[] thetaHatStar) compute variance of a statistic thetaHat
static double[]	efronCI(double level, double[] thetaHatStar) compute approximate central confidence interval for thetaHat (Efron percentile method)
static double[]	efronCI(double level, double[] thetaHatStar, int[] array) compute approximate central confidence interval for thetaHat (Efron percentile method)
static double[]	hallCI(double level, double thetaHat, double[] thetaHatStar) compute approximate central confidence interval for thetaHat (Hall percentile method)
static double[]	hallCI(double level, double thetaHat, double[] thetaHatStar, int[] array) compute approximate central confidence interval for thetaHat (Hall percentile method)

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

BootstrapStatistics

public BootstrapStatistics()

Method Detail

computeBIAS

public static double computeBIAS(double thetaHat,
                                 double[] thetaHatStar)

compute bias of a statistic thetaHat in estimating the true theta

Parameters:

thetaHat - the statistic

thetaHatStar - bootstrap replicates of thetaHat

Returns:

estimate of bias (notation: BIAS with hat)

biasCorrectedEstimate

public static double biasCorrectedEstimate(double thetaHat,
                                           double[] thetaHatStar)

correct a statistic thetaHat for its bias

Parameters:

thetaHat - the statistic

thetaHatStar - bootstrap replicates of thetaHat

Returns:

bias-corrected estimate

computeVAR

public static double computeVAR(double[] thetaHatStar)

compute variance of a statistic thetaHat

Parameters:

thetaHatStar - bootstrap replicates of statistic thetaHat

Returns:

estimate of variance of thetaHat (notation: VAR with hat)

computeSD

public static double computeSD(double[] thetaHatStar)

compute standard error (accuracy) of a statistic thetaHat

Parameters:

thetaHatStar - bootstrap replicates of statistic thetaHat

Returns:

estimate of standard error of thetaHat (notation: SD with hat)

efronCI

public static double[] efronCI(double level,
                               double[] thetaHatStar)

compute approximate central confidence interval for thetaHat (Efron percentile method)

Parameters:

level - confidence level (e.g., 0.95)

thetaHatStar - bootstrap replicates of statistic thetaHat

Returns:

confidence set (array of two doubles)

efronCI

public static double[] efronCI(double level,
                               double[] thetaHatStar,
                               int[] array)

compute approximate central confidence interval for thetaHat (Efron percentile method)

Parameters:

level - confidence level (e.g., 0.95)

thetaHatStar - bootstrap replicates of statistic thetaHat

array - helper integer array (same length as thetaHatStar)

Returns:

confidence set (array of two doubles)

hallCI

public static double[] hallCI(double level,
                              double thetaHat,
                              double[] thetaHatStar)

compute approximate central confidence interval for thetaHat (Hall percentile method)

Parameters:

level - confidence level (e.g., 0.95)

thetaHat - the statistic

thetaHatStar - bootstrap replicates of statistic thetaHat

Returns:

confidence set (array of two doubles)

hallCI

public static double[] hallCI(double level,
                              double thetaHat,
                              double[] thetaHatStar,
                              int[] array)

compute approximate central confidence interval for thetaHat (Hall percentile method)

Parameters:

level - confidence level (e.g., 0.95)

thetaHat - the statistic

thetaHatStar - bootstrap replicates of statistic thetaHat

array - helper integer array (same length as thetaHatStar)

Returns:

confidence set (array of two doubles)